Title: A comparative study of finite element method for the numerical solution of reaction-diffusion problem

Authors: Nini Maharana; Ameeya Kumar Nayak

Addresses: Department of Mathematics, Ravenshaw University, Cuttack, Odisha, 753003, India ' Department of Mathematics, IIT Roorkee, Roorkee, 247667, India

Abstract: This paper presents a least-squares finite element approach for the solution of reaction-diffusion pellet problem for slab geometry by considering some special types of reactions which are applicable for chemical transformation of natural gas components. The nonlinear terms are treated with Newton's linearisation technique. A detailed comparison with other weighted residual methods such as collocation, sub-domain and Galerkin methods are also examined. The issues related to chemical reactor problems and their error analysis is discussed both theoretically and numerically. The least-squares method suffers convergency effect by using the Picard's method instead of Newton's iteration method as obtained by Galerkin and orthogonal collocation methods.

Keywords: least square method; weighted residuals; diffusion reaction equation; slab model.

DOI: 10.1504/IJCSM.2017.083741

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.2, pp.101 - 114

Received: 20 Apr 2015
Accepted: 17 Jun 2016
Published online: 21 Apr 2017 *

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